Common Center Of Mass Research Articles

Deviations from the universal Initial Mass Function in binary star clusters

Abstract The stellar mass distribution in star-forming regions, stellar clusters and associations, the Initial Mass Function (IMF), appears to be invariant across different star-forming environments, and is consistent with the IMF observed in the Galactic field. Deviations from the field, or standard, IMF, if genuine, would be considered strong evidence for a different set of physics at play during the formation of stars in the birth region in question. We analyse N-body simulations of the evolution of spatially and kinematically substructured star-forming regions to identify the formation of binary star clusters, where two (sub)clusters which form from the same Giant Molecular Cloud orbit a common centre of mass. We then compare the mass distributions of stars in each of the subclusters and compare them to the standard IMF, which we use to draw the stellar masses in the star-forming region from which the binary cluster(s) form. In each binary cluster that forms, the mass distributions of stars in one subcluster deviates from the standard IMF, and drastically so when we apply similar mass resolution limits as for the observed binary clusters. Therefore, if a binary subcluster is observed to have an unusual IMF, this may simply be the result of dynamical evolution, rather than different physical conditions for star formation in these systems.

Rotating solutions to the incompressible Euler–Poisson equation with external particle

We consider a two-dimensional, incompressible fluid body, together with self-induced interactions. The body is perturbed by an external particle with small mass. The whole configuration rotates uniformly around the common center of mass. We construct solutions, which are stationary in a rotating coordinate system, using perturbative methods. In addition, we consider a large class of internal motions of the fluid. The angular velocity is related to the position of the external particle and is chosen to satisfy a non-resonance condition.

Numerical Analysis of the Influence of a Magnetic Field on the Group Dynamics of Iron-Doped Carbon Nanotori

Columnar phases consisting of a group of carbon toroidal molecules (C120, C192, C252, C288) are studied numerically. Each nanotorus was previously doped with an iron atom. This made it possible to use an external magnetic field as a tool for influencing both an individual molecule and a linear fragment of the columnar phase. A high-precision scheme for calculating the dynamics of large molecules with a rigid frame structure is proposed to solve the problem. The group dynamics of nanotori clusters under the influence of an external magnetic field has been studied using classical molecular dynamics methods. The influence of the molecular cluster size, temperature, magnetic moment of the molecule, and magnetic field direction on the collective behavior of iron-doped toroidal molecules with different contents of carbon atoms is analyzed. Molecular dynamics calculations showed that systems of nanotori doped with a single iron atom retain a columnar structure both in the absence and in the presence of an external magnetic field. The columnar fragment behaves as a stable linear association of molecules even at sufficiently high values of magnetic induction, performing a coordinated collective orbital rotation around a common center of mass on a nanosecond time scale.

Classical nonrelativistic fractons

We initiate the study of the classical mechanics of nonrelativistic fractons in its simplest setting—that of identical one-dimensional particles with local Hamiltonians characterized by a conserved dipole moment in addition to the usual symmetries of space and time translation invariance. We introduce a family of models and study the N-body problem for them. We find that locality leads to a “Machian” dynamics in which a given particle exhibits finite inertia only if within a specified distance of another particle. For well-separated particles, this dynamics leads to immobility, much as for quantum models of fractons discussed before. For two or more particles within inertial reach of each other at the start of motion, we obtain an interesting interplay of inertia and interactions. Specifically, for a solvable “inertia only” model of fractons, we find that two particles always become immobile at long times. Remarkably, three particles generically evolve to a late time state with one immobile particle and two oscillating about a common center of mass with generalizations of such “Machian clusters” for N>3. Interestingly, these Machian clusters exhibit physical limit cycles in a Hamiltonian system even though mathematical limit cycles are forbidden by Liouville's theorem. Published by the American Physical Society 2024

Mass formulas for individual black holes in merging binaries

We give formulas for individual black hole masses in a merger, by using Newtonian physics, in terms of the three measured quantities in the detector: the initial wave frequency f 1, the maximum detected frequency (chirp frequency) f 2, and the time elapse τ between these two frequencies. Newtonian gravity provides an excellent pedagogical tool to understand the basic features of gravitational wave observations, but it must be augmented with the assumption of gravitational radiation from General Relativity for accelerating masses as there is no gravitational wave Newtonian gravity. The simplest approach would be to consider a binary system of two non-spinning masses (two black holes) circling their common center of mass. All the computations can be done within Newtonian physics, but the General Relativistic formula for the power carried by gravitational waves is required in this scheme. It turns out there is a subtle point: for the consistency of this simple, yet pedagogical computation, taking the lowest order power formula from General Relativity leads to complex individual masses. Here we remedy this problem and suggest a way to write down an average power formula coming from perturbative General Relativity.

The concentric Sitnikov problem: Circular case

A new configuration in the sense of concentric Sitnikov problem is introduced in this paper. This configuration consists of four primaries Pi(i=1,2,3,4) of masses mi, respectively. Here, all the primaries are placed on a straight line and moving in concentric circular orbits around their common center of mass under the restrictions of masses as m1=m2=m, m3=m4=ḿ and m>ḿ. The objective of the present manuscript is to study the existence of equilibrium points and their linear stability, first return map, periodic orbits, and N-R BoA in the proposed model. Under the restriction of mass parameter 0<μ́<1/4, it is found that there exist three equilibrium points and all the equilibrium points are linearly unstable for all values of mass parameter 0<μ́<1/4. Graphically, the nature of orbits have been examined with the help of first return map. The families of periodic orbits of infinitesimal mass m5 around the primaries and equilibrium points have been obtained for different values of mass parameter μ́. Finally, we explore the Newton–Raphson Basins of Attraction (N-R BoA), related to the equilibrium points in the concentric problem of Sitnikov.

Superposing tidal force fields

The motion of the Earth relative to the Sun’s inertial frame of reference, is a superposition of the motion of the Earth around the common center of mass of the Moon and the Earth and the motion of that center of mass around the Sun. However, you get the resulting tidal force field due to the simultaneous existence of the Moon and the Sun by superposing a Moon- induced tidal force field and a Sun-induced tidal force field. Where, the Moon-induced tidal force field is calculated as if the Sun were not existing, and the Sun-induced tidal force field is calculated as if the Moon were not existing. The situation may lead to confusion. Thus, we give a formal conceptual account of the state of affairs, and argue that the case is useful when introducing undergraduates to inertial forces and understanding Newtonian mechanics.

Beyond Coulomb’s Law: The Interaction Between Overlapping Charged Balls

We give a detailed analysis of the interaction between overlapping charged balls, depending on the distance between them and their sizes. If one of the balls is entirely inside another ball, the interaction force is strictly proportional to the distance between the balls’ centers. This force has a maximum when some partial balls overlap depending on the ratio of their radii. For example, if the balls are the same, then the maximum corresponds to the distance between the centers equal to the balls’ radius. At small relative displacements of oppositely charged balls, they should perform harmonic oscillations around their common center of mass. The paper is addressed to undergraduates who deal with modern electrostatics.

Halo Orbits under Some Perturbations in cr3bp

The general idea of this paper is to study the effect of mass variation of a test particle on periodic orbits in the restricted three-body model. In the circular restricted three-body problem (cr3bp), two bigger bodies (known as primary and secondary or sometime only primaries) are placed at either side of the origin on abscissa while moving in circular orbits around their common center of mass (here origin), while the third body (known as smallest body or infinitesimal body or test particle) is moving in space and varies its mass according to Jeans law. Using the Lindstedt–Poincaré method, we determine equations of motion and their solutions under various perturbations. The time-series and halo orbits around one of the collinear critical points of this model are drawn under the effects of the solar radiation pressure of the primary and the oblateness of the secondary. In general, these two dynamical properties are symmetrical.

An Early Catalog of Planet-hosting Multiple-star Systems of Order Three and Higher

We present a catalog (status 2022 July 1) of triple and higher-order systems identified containing exoplanets based on data from the literature, including various analyses. We explore statistical properties of the systems with a focus on both the stars and the planets. So far, about 30 triple systems and one to three quadruple systems, including (mildly) controversial cases, have been found. The total number of planets is close to 40. All planet-hosting triple-star systems are highly hierarchic, consisting of a quasi-binary complemented by a distant stellar component, which is in orbit about the common center of mass. Furthermore, the quadruple systems are in fact pairs of close binaries (“double–doubles”), with one binary harboring a planet. For the different types of star–planet systems, we introduce a template for the classifications of planetary orbital configurations in correspondence to the hierarchy of the system and the planetary host. The data show that almost all stars are main-sequence stars, as expected. However, the stellar primaries tend to be more massive (i.e., corresponding to spectral types A, F, and G) than expected from single-star statistics, a finding also valid for stellar secondaries but less pronounced. Tertiary stellar components are almost exclusively low-mass stars of spectral type M. Almost all planets have been discovered based on either the Radial Velocity method or the Transit method. Both gas giants (the dominant type) and terrestrial planets (including super-Earths) have been identified. We anticipate the expansion of this database in the light of future planetary search missions.

Kinematic and dynamic parameters of final stage of javelin throwing

Javelin throwing characterizes by creation of dynamic effort in shoulder-girdle during the process of movement. The emergence of excessive efforts in the joints of the parts of the body performing this sport exercise leads often to injury to the athlete. In this regard, the actual direction of training and competitive activity is the coordination and rationalization of movements in accordance with the principle of bionic adequacy of the system (in this case, “thrower – javelin”), the result of which is the maximum effectiveness of the exercise in the absence of traumatic effects of loads and movements. Biomechanical analysis of the final stage of javelin throwing was performed on the basis of 659 videos of competitive attempts. The results of measuring the angular displacements of the links of the body relative to each other and the common center of mass of the body in various nodal elements of motion are presented. In the work, the method of posture reference points of movements was used, which made it possible to distinguish starting and final movements, as well as a number of animated positions. Prediction of changes in the position of the body links taking into account the moments and radius of inertia of the links relative to the general center of mass of the thrower body allow us to take preventive measures to exclude deviations from the given optimal trajectory of the body parts. The determination of the ranges of angular positions in the joints of the parts of the body also contributes to the achievement of high sports results.

Enhancement of double-close-binary quadruples

ABSTRACT Double-close-binary quadruples (2 + 2 systems) are hierarchical systems of four stars where two short-period binary systems move around their common centre of mass on a wider orbit. Using Gaia Early Data Release 3, we search for comoving pairs where both components are eclipsing binaries. We present eight 2 + 2 quadruple systems with inner orbital periods of &amp;lt;0.4 d and with outer separations of ≳1000 au. All of these systems but one are newly discovered by this work, and we catalogue their orbital information measured from their light curves. We find that the occurrence rate of 2 + 2 quadruples is 7.3 ± 2.6 times higher than what is expected from random pairings of field stars. At most a factor of ∼2 enhancement may be explained by the age and metallicity dependence of the eclipsing binary fraction in the field stellar population. The remaining factor of ∼3 represents a genuine enhancement of the production of short-period binaries in wide-separation (&amp;gt;103 au) pairs, suggesting a close-binary formation channel that may be enhanced by the presence of wide companions.

Intruders cooperatively interact with a wall into granular matter

When a cylindrical object penetrates granular matter near a vertical boundary, it experiences two effects: its center of mass moves horizontally away from the wall, and it rotates around its symmetry axis. Here we show experimentally that, if two identical intruders instead of one are released side-by-side near the wall, both effects are also detected. However, unexpected phenomena appear due to a cooperative dynamics between the intruders. The net horizontal distance traveled by the common center of mass of the twin intruders is much larger than that traveled by one intruder released at the same initial distance from the wall, and the rotation is also larger. The experimental results are well described by the Discrete Element Method (DEM), which reveals that, as the number of intruders horizontally released side-by-side increases, the total energy dissipation per intruder decreases. Finally, DEM simulations demonstrate that the horizontal repulsion is substantially enhanced if groups of intruders are released forming a column near the wall.

Süreksiz Referans Sinyalleri ile İnsan Sinovyal Sıvısında Birden Fazla Biyohibrit Mikrorobotun Hareket Kontrolü için Benzetim Çalışmaları

It is envisioned that biomedical swarms are going to be used for therapeutic operations in the future. The utilization of a single robot in live tissue is not practical because of the limited volume. In contrast, a large group of microrobots can deliver a useful amount of potent chemicals to the targeted tissue. In this simulation study, a trio of magnetotactic bacteria as a task-force, Magnetospirillum Gryphiswaldense MSR-1, is maneuvered via adaptive micro-motion control through an external magnetic field. The magnetic field is induced by a single permanent magnet positioned by an open kinematic chain. The coupled dynamics of this small group in the human synovial tissue is simulated with actual magnetic and fluidic properties of the synovial liquid. The common center of mass is tracked by the equation of motion. The overall hydrodynamic interaction amongst all three bacteria is modeled within a synovial medium confined with flat surfaces. A bilateral control scheme is implemented on top of this coupled model. The position of the common center of mass is used as the reference point to the end-effector of the robotic arm. The orientation of the magnetic field is rotated to change the heading of the bacterial-group in an addressable manner. It has been numerically observed that controlling the common swimming direction of multiple bacteria is fairly possible. Results are presented via the rigid-body motion of the robotic task-force as well as the fluidic and magnetic force-components acting on the bacteria along with the bilateral control effort in all axes.

NGTS clusters survey – III. A low-mass eclipsing binary in the Blanco 1 open cluster spanning the fully convective boundary

ABSTRACT We present the discovery and characterization of an eclipsing binary identified by the Next Generation Transit Survey in the ∼115-Myr-old Blanco 1 open cluster. NGTS J0002−29 comprises three M dwarfs: a short-period binary and a companion in a wider orbit. This system is the first well-characterized, low-mass eclipsing binary in Blanco 1. With a low mass ratio, a tertiary companion, and binary components that straddle the fully convective boundary, it is an important benchmark system, and one of only two well-characterized, low-mass eclipsing binaries at this age. We simultaneously model light curves from NGTS, TESS, SPECULOOS, and SAAO, radial velocities from VLT/UVES and Keck/HIRES, and the system’s spectral energy distribution. We find that the binary components travel on circular orbits around their common centre of mass in Porb = 1.098 005 24 ± 0.000 000 38 d, and have masses Mpri = 0.3978 ± 0.0033 M⊙ and Msec = 0.2245 ± 0.0018 M⊙, radii Rpri = 0.4037 ± 0.0048 R⊙ and Rsec = 0.2759 ± 0.0055 R⊙, and effective temperatures $T_{\rm pri}=\mbox{$3372\, ^{+44}_{-37}$}$ K and $T_{\rm sec}=\mbox{$3231\, ^{+38}_{-31}$}$ K. We compare these properties to the predictions of seven stellar evolution models, which typically imply an inflated primary. The system joins a list of 19 well-characterized, low-mass, sub-Gyr, stellar-mass eclipsing binaries, which constitute some of the strongest observational tests of stellar evolution theory at low masses and young ages.

The Motion of Out-of-Plane Equilibrium Points in the Elliptic Restricted Three-Body Problem at &lt;i&gt;J&lt;sub&gt;4&lt;/sub&gt;&lt;/i&gt;

We have investigated the motion of the out-of-plane equilibrium points within the framework of the Elliptic Restricted Three-Body Problem (ER3BP) at J4 of the smaller primary in the field of stellar binary systems: Xi- Bootis and Sirius around their common center of mass in elliptic orbits. The positions and stability of the out-of-plane equilibrium points are greatly affected on the premise of the oblateness at J4 of the smaller primary, semi-major axis and the eccentricity of their orbits. The positions L6, 7 of the infinitesimal body lie in the xz-plane almost directly above and below the center of each oblate primary. Numerically, we have computed the positions and stability of L6, 7 for the aforementioned binary systems and found that their positions are affected by the oblateness of the primaries, the semi-major axis and eccentricity of their orbits. It is observed that, for each set of values, there exist at least one complex root with positive real part and hence in Lyapunov sense, the stability of the out-of-plane equilibrium points are unstable.

Shear dynamics of polydisperse double emulsions

We numerically study the dynamics of a polydisperse double emulsion under a symmetric shear flow. We show that both dispersity and shear rate crucially affect the behavior of the innermost drops and of the surrounding shell. While at low/moderate values of shear rates, the inner drops rotate periodically around a common center of mass triggered by the fluid vortex formed within the emulsion generally regardless of their polydispersity; at higher values, such dynamics occurs only at increasing polydispersity, since monodisperse drops are found to align along the shear flow and become approximately motionless at late times. Our simulations also suggest that increasing polydispersity favors close-range contacts among cores and persistent collisions, while hindering shape deformations of the external droplet. A quantitative evaluation of these effects is also provided.

Balancing of the Orthoglide Taking into Account Its Varying Payload

For fast-moving robot systems, the fluctuating dynamic loads transmitted to the supporting frame can excite the base and cause noise, wear, and fatigue of mechanical components. By reducing the shaking force completely, the dynamic characteristics of the robot system can be improved. However, the complete inertial force and inertial moment balancing can only be achieved by adding extra counterweight and counter-rotation systems, which largely increase the total mass, overall size, and complexity of robots. In order to avoid these inconveniences, an approach based on the optimal motion control of the center of mass is applied for the shaking force balancing of the robot Orthoglide. The application of the “bang–bang” motion profile on the common center of mass allows a considerable reduction of the acceleration of the total mass center, which results in the reduction of the shaking force. With the proposed method, the shaking force balancing of the Orthoglide is carried out, taking into account the varying payload. Note that such a solution by purely mechanical methods is complex and practically inapplicable for industrial robots. The simulations in ADAMS software validate the efficiency of the suggested approach.

Sitnikov five-body problem with combined effects of radiation pressure and oblateness

We study the motion of negligible mass in the frame work of Sitnikov five-body problem where four equal oblate spheroids known as primaries symmetrical in all respect are placed at the vertices of square. These primaries are also considered as source of radiations moving in a circular orbit around their common center of mass. The fifth negligible mass performs oscillations along z-axis which is perpendicular to the orbital plane of motion of the primaries and passes through the center of mass of the primaries. Under the combined effects of radiation pressure and oblateness, we have developed the series solution by the Lindstedt-Poincare technique and established averaged Hamiltonians by applying the Van der Pol transformation and averaging technique of Guckenheimer and Holmes (1983). The orbits such as regular, periodic, quasi-periodic, chaotic, or stochastic have been examined with the help of Poincare surfaces of section.

Motion of the Infinitesimal Variable Mass in the Generalized Circular Restricted Three-Body Problem under the Effect of Asteroids Belt

The present paper deals with the study of the motion’s properties of the infinitesimal variable mass body moving in the same orbital plan as two massive bodies (considered as primaries). It is assumed that the massive bodies have radiating effects, have oblate shapes, and are moving in circular orbits around their common center of mass. Using the procedures established by Singh and Abouelmagd, we determined the equations of motion of the infinitesimal body for which we assumed that under the effects of radiation and oblateness of the primaries, its mass varies following Jean’s law. We evaluated analytically and numerically the locations of equilibrium points and examined the stability of these equilibrium points. Finally, we found that all the points are unstable.